ESTIMATION OF HOUSEHOLD DEMAND
SYSTEMS WITH THEORETICALLY COMPATIBLE
ENGEL CURVES AND UNIT VALUE
SPECIFICATIONS
Ian Crawford
François Laisney
Ian Preston
THE INSTITUTE FOR FISCAL STUDIES
WP02/17
Estimation of Household Demand Systems with
Theoretically Compatible Engel Curves and Unit
Value Specifications
Ian Crawford∗, François Laisney†& Ian Preston‡.
June 2002
Abstract
We develop a method for estimation of price reactions using unit value
data which exploits the implicit links between quantity and unit value
choices. This allows us to combine appealing Engel curve specifications
with a model of unit value determination in a way which is consistent
with demand theory, unlike methods hitherto prominent in the literature. The method is applied to Czech data.
Key Words: Consumer demand, unit values
JEL Classification: D11, D12
Acknowledgements:
We are grateful for comments and advice from two anonymous referees, as well as from Richard Blundell, Fiona Coulter, Angus Deaton,
Philippe De Vreyer, Bas Donkers, Vera Kameničkova, Colin Lawson,
Arthur Lewbel, Thierry Magnac, Edmond Malinvaud, Costas Meghir,
Daniel Munich, Jean-Marc Robin, David Ulph, Jiřı̀ Večernik, Frank
Windmeijer, and participants at conferences in Istanbul, Leuven, Mannheim, Prague and various seminars. This research was undertaken with
support from two programmes of the European Commission: PHAREACE (project “Tax Policy During Economic Transition”) and HCM
(project “Microeconometrics of Public Policy Issues”). All errors remain our own.
∗
Institute for Fiscal Studies.
Email: ian [email protected]
†
BETA-THEME, Université Louis Pasteur, Strasbourg and ZEW, Mannheim.
Email: [email protected]
‡
University College London and Institute for Fiscal Studies.
Email: [email protected]
1
Executive Summary
One of the main difficulties in the estimation of demand systems using household data concerns the precise estimation of price reactions. The
reason is that, whereas data on households normally exhibit considerable
variation in expenditures, this is not typically the case for prices. Very often information about geographical variation in prices or variation over time
within the period covered by one cross-section is lacking, so that prices are
assumed uniform over all households of the same cross-section.
Data sets which contain information, not only on expenditures, but also
on quantities consumed for a set of goods, offer interesting possibilities: this
allows the computation of individual unit values for the spending of each
household on any of these goods. It might be thought possible to model
demand for these goods treating these unit values as prices. These would
appear much more attractive for estimation purposes than aggregate prices,
which are just averages that no household actually pays. Yet, since the goods
are invariably subject to some degree of aggregation, it is undoubtedly true
that much of the variation in unit values will actually result from household
choice regarding the nature of the goods purchased.
We develop a method for estimation of price reactions using unit value
data which exploits the implicit links between quantity and unit value choices
and which builds on methods previously proposed in the demand literature.
This allows us to combine appealing Engel curve specifications with a model
of unit value determination in a way which is consistent with demand theory,
unlike methods hitherto prominent in the literature.
We illustrate the technique with an application to Czech Family Budget
Survey data.
2
1
Introduction
One of the main difficulties in the estimation of demand systems using
household data concerns the precise estimation of price reactions. While
requiring care in the treatment of endogeneity, income effects are more easily estimated. Yet unless, say, one is prepared to make strong assumptions
on functional form which result in a connection between price and income
effects, but which, if wrong, produce important biases in the estimation of
price elasticities (see e.g. Deaton and Muellbauer, 1980), price effects are
difficult to capture. The reason is that, whereas data on households normally
exhibit considerable variation in expenditures, this is not typically the case
for prices. Very often information about geographical variation in prices or
variation over time within the period covered by one cross-section is lacking,
so that prices are assumed uniform over all households of the same crosssection. Indeed most studies based on the Family Expenditure Survey for
instance, a long series of cross-sections of UK households, have relied solely
on year-to-year variation of prices under that assumption (see e.g. Banks,
Blundell and Lewbel, 1996). In the absence of such long series, researchers
have often resorted to combining a small number of cross-sections with aggregate time series data, the idea being basically to identify the income
effects from the cross-sectional data and the price effects from the aggregate
data (examples of studies relying on that strategy are Stone, 1954, Jorgenson, Lau and Stoker, 1982, and Nichèle and Robin, 1995). Note that Lewbel
(1989) proposes an original approach to the identification and estimation of
demand systems on pure cross-section data (without any price variation).
Considering two levels of aggregation, under the assumption of homothetic
weak separability Lewbel’s approach imposes no restriction on functional
form at the higher level. We shall draw parallels between his approach and
3
ours later.
Data sets which contain information, not only on expenditures, but also
on quantities consumed for a set of goods, offer interesting possibilities: this
allows the computation of individual unit values for the spending of each
household on any of these goods. It might be thought possible to model
demand for these goods treating these unit values as prices. These would
appear much more attractive for estimation purposes than aggregate prices,
which are just averages that no household actually pays. Yet, since the goods
are invariably subject to some degree of aggregation, it is undoubtedly true
that much of the variation in unit values will actually result from household
choice regarding the nature of the goods purchased.
Deaton (1987, 1988, 1990, 1997) has developed a way of modelling price
reactions jointly with choice of unit values in data of this type, under assumptions about fixity of underlying relative prices within spatially defined
areas. The model suffers however from reliance on an approximation which
is only compatible everywhere with demand theory for the theoretically unappealing loglinear demand specification. We develop an alternative, but
related, approach which exploits the implicit links between quantity and
unit value choices. This marks an advance on previous work in allowing
in principle for appealing Engel curve specifications to be combined with a
model of unit value determination in a way which is fully consistent with
demand theory.
We illustrate the technique with an application to Czech Family Budget Survey data which has the feature that the geographical location of
households is fairly precise. The preference specification used is a linear approximation of the Almost Ideal Demand (AID) system and the eight goods
categories retained are six categories of food, plus clothing and footwear. In
4
order to avoid unnecessary separability assumptions, the demand system is
estimated conditionally on expenditures on several other good categories,
on durable ownership and on labour market status. The results are encouraging, and our approach has subsequently been applied with success in the
context of the estimation of heterogeneous labour demand functions by De
Vreyer (2000).
Section 2 discusses relevant points from demand theory. Section 3 outlines a three stage estimation methodology. Section 4 describes the Czech
data used and Section 5 presents illustrative results.
2
Demand and unit values
We start by developing an approach to modelling the determination of unit
values. Our assumptions and notation follow those of Deaton’s several papers on the subject. For the purpose of empirical investigation, goods are
taken to be organised into m groups such as meat, fish, clothes and so on.
Consumption within a group G is a vector of quantities qG with unobserved
prices pG . The consumer’s total budget is X.
What we attempt to model is the determination of an observed group
quantity index QG , defined by
QG ≡ 10G qG ,
(1)
where 10G is a vector of ones1 and observed group spending xG ≡ p0G qG from
which together we can calculate a unit value VG ≡ xG /QG .
Households reside within identifiable regional clusters and two central assumptions are made regarding the spatial variation in the unobserved prices.
1
For simplicity, we assume, without loss of generality, that qG is measured in the units
chosen for aggregation by the data collector (like weight for meat or pairs for shoes).
5
Firstly, we assume that relative prices within each group are fixed everywhere, so that pG = πG p0G , where πG is defined as a scalar (Paasche) linear
homogeneous price level for the group (for instance, the price of meat), and
p0G is a vector representing the fixed within-group relative price structure
(for instance, the relative prices of different types and qualities of meat).
This assumption will allow us to treat group G as a Hicks aggregate, so that
qG will be a function of total spending X and of the vector π of group price
levels (generally, omission of a G subscript for a group variable will denote
the vector of values for all groups).2 As a consequence, QG , xG and VG , as
well as related variables such as budget shares, wG ≡ xG /X, can also be
written in this way. Secondly, the price vector π is assumed constant within
the spatial clusters, though allowed to vary between clusters, so that we will
use the notation π c for clusters c = 1, . . . , C.
Deaton’s approach is to estimate the within-cluster relationships whereby
QG (or xG or wG ) and VG are determined as functions of X, and then to
use cross-equation restrictions to recover structural price parameters from
the between-cluster correlations between the residuals. We argue that this
method is theoretically convincing only for a particular and unattractive
demand specification, specifically loglinear demands. The strength of the
cross-equation restrictions between the QG and VG equations rules out mutually consistent specifications for the two if adopting specifications with
more attractive Engel curves. We suggest an alternative approach, which
combines the advantage of more general theoretical consistency and greater
computational convenience.
2
The assumption appears very strong, but Lewbel (1996) shows that this type of aggregation will be possible under the much weaker assumption of stochastic independence
between πG and the vector of relative prices pG /πG . This will be the case, at least approximately, if the relative prices are stationary over time, whereas πG is not. We will
come back to this assumption when discussing the stochastic structure of the econometric
specification.
6
Assuming weak separability of preferences in the partition corresponding
to groups 1, . . . , G, . . . , m, and using homogeneity, we can write
qG = fG (xG , pG )
= fG (VG QG /πG , p0G ).
(2)
Suppressing p0G (given that it is fixed) and noting that VG /πG then depends
only on qG , we can write
VG = πG hG (VG QG /πG )
(3)
which defines an implicit relationship between VG /πG and QG . The fact that
the unit values are independent of the component items given πG and QG
does not require any assumption that goods are consumed in fixed proportions — indeed that assumption would have the much stronger consequence
that VG would be constant. This equation, which makes clear the crossequation restrictions on the functional forms of quantity and unit value
equations, is central to our treatment. It implies the equation
∂ ln VG /∂ ln πH − 1[G=H]
∂ ln QG /∂ ln πH
=
,
∂ ln VG /∂ ln X
∂ ln QG /∂ ln X
(4)
used by Deaton to derive price elasticities at the second stage of his estimation procedure, and can therefore be seen as implicitly underlying his results
although not explicitly stated. This follows from
µ
¶
∂ ln VG
∂ ln VG
∂ ln QG
h
− 1[G=H] = eG
+
− 1[G=H] ,
∂ ln πH
∂ ln πH
∂ ln πH
µ
¶
∂ ln VG ∂ ln QG
∂ ln VG
= ehG
+
,
∂ ln X
∂ ln X
∂ ln X
where ehG denotes the elasticity of hG (.) with respect to its (scalar) argument,
and is a consequence of the separability assumptions made, and not simply
of definitions.
If both the quantity and unit value relationships are specified to be double logarithmic, then this specification is compatible with (3). Yet there
7
are very strong restrictions on the coefficients: if ln QG = αG + βG ln X +
P
P
H γGH ln πH and ln VG − ln πG = aG + bG ln X +
H cGH ln πH , then by
(4) βG /bG = γGH /cGH for all H. Even without these, the double logarithmic specification is very unsatisfactory: loglinear demands do not satisfy
adding up and cannot capture zero demands. This is worrying since major difficulties arise if the method is applied with other functional forms.
If, for instance, an AID type budget share equation — with w linear in
ln X and lnπ — is adopted while the log unit value is also specified linearly in the same variables, this is not compatible with (3) (except under
extremely strong restrictions, see Appendix A for details). This specification has been adopted in Deaton (1990), Deaton and Grimard (1991) and
Ayadi, Baccouche, Goaied and Matoussi (1995). In none of these papers is
the incompatibility explicitly recognised, although Deaton (1997) suggests
that it might be appropriate to use (4) at mean sample, assuming constancy
of elasticities as a reasonable approximation to the truth.
From (3) it follows that, given a functional form φ for budget shares, one
would need to estimate a consistent system
wG
= φG (X, π) ,
ln VG = ln πG + ln hG
·
¸
X
φG (X, π) .
πG
(5)
A simple linear specification in ln X and lnπ for the share equation therefore
requires a unit value equation which will be non-linear in these variables.
The problem here is that, once the quantity or budget share relationship is
specified, (3) imposes too many cross-equation restrictions to permit also an
unrestricted dependence of unit values on X and π.
This paper aims to make an advance toward the important goal of developing a simple theory-consistent method capable of handling more plausible
Engel curves. Our central suggestion is to specify the quantity or bud8
get share relationship, φG (X, π), and then to derive a relationship between
VG and QG from an independent specification of (3) (since the form of hG
is unrestricted). In the case of homothetic within-group demands (2) and
therefore constant within-group budget shares, hG is constant and VG is
therefore proportional to πG .3 More generally, hG will be increasing if more
expensive goods within group G tend to be income elastic and decreasing if
they tend to be income inelastic. In some cases it will be possible to write
VG = πG ψG (QG ) for some function ψG . To be more specific, for example, a
specification
ln VG = aG + bG ln QG + ln πG ,
(6)
which would arise from assuming hG (VG QG /πG ) = AG (VG QG /πG )BG , where
bG = AG /(1 − AG ) and aG = (1 + bG ) ln BG , is generally admissible on theoretical grounds. In addition to its theoretical consistency, the absence from
the unit value equation of terms in πH for H 6= G and the known unitary
elasticity with respect to πG considerably simplify estimation of structural
parameters, as will be apparent below.
3
Specification and estimation
Following Deaton, we will choose for our specification of the budget shares
the approximate AID model with a log-linear approximation to the log price
index. Clearly, using the full AID specification, or even some quadratic extension thereof (see e.g. Banks, Blundell and Lewbel, 1997), would yield a
superior specification, but the implied non linearity would defeat the withincluster estimation strategy adopted below. Thus, while we achieve theoretical consistency in the specification of the unit value equation, we only have
an approximation thereof in the specification of the share equation — al3
This is pointed out by De Vreyer (2000).
9
though arguably quite a good one (although Pashardes, 1993, documents
problems with this approximation). The share equation for category G,
demanded by household h in cluster c, is thus given by
h
wG
= α0G + Zh αG +
X
c
γGH ln πH
+ βG ln x̌h + uhG
(7)
H
P
c ,
where x̌h is deflated expenditure, ln x̌h ≡ ln X h −ln P c ≡ ln X h − H λH ln πH
P c is a cluster price index for suitably chosen weights.4 This leads to the
equation
h
wG
= α0G + Zh αG +
X
c
δGH ln πH
+ βG ln X h + uhG ,
(8)
H
with δGH = γGH −βG λH . Vector Zh includes socio-demographic characteristics as well as further conditioning variables, mentioned in the introduction,
and which will be described in the next section. Several of these are potentially endogenous and will be instrumented.
For (6) we assume that the unit value equation is of the form
c
h
ln VGh = a0G + Zh aG + ln πG
+ bG ln QhG + vG
.
(9)
We assume independence between observations. This may appear unduly
restrictive, as it rules out the presence of cluster effects. But firstly, we have
to rule out the simultaneous appearance of cluster effects in both share and
unit value equations, as this would preclude the identification of the price
effects. Secondly, allowing cluster effects in the share equation only would
not change anything in the sequel, provided these effects were independent
4
While it would clearly be preferable to allow the weights of the price index to be
cluster-specific, the following points can be made. Firstly, the existence of a cluster price
index does not conflict with the recognition that unit values are household-specific. Secondly, the true underlying prices should be constant within clusters by the law of one
price, even if unit values are not. Finally, it is only the weights which are constant across
clusters and not the price index itself, and this represents already a substantial improvement on the typical treatment of prices as constant across the whole territory. In our
empirical work a cluster will be defined as a spatial unit at a point in time
10
of π. This is where Lewbel’s assumption is helpful again: allowing the (unobserved) relative prices p0G to vary across clusters — and thus become p0c
G
c
— introduces a cluster effect; assuming independence between p0c
G and π
makes this cluster effect innocuous.5 And thirdly, postulating additive errors
in these equations is questionable anyway, as equation (5) suggests.
³ 0
´
0 0
The covariance matrix Ω of the vectors uh , vh is assumed constant
across observations and otherwise unrestricted. This homoscedasticity assumption is less plausible for log unit values than it is for budget shares,
but we reckon that it would be difficult to relax it in the unit value model,
as should become apparent below.
A first strategy might be to estimate (8) replacing prices with unit values
while instrumenting the latter. An approach of this type has been adopted
by Pitt (1983) and Strauss (1982). The implicit assumption of such an
approach is that the vector of unit values Vh can be treated simply as an
error-ridden observation of the price vector π c , with a measurement error
that is independent of π c . In the context of our unit value model such
an approach will be badly misspecified if bG is not equal to zero in (9), in
c will depend on the outlay X h and the vector
which case the ratios VGh /πG
π c of price indices. In such circumstances the parameters of (8) will not be
properly recovered under the naive approach.
The estimation proceeds in three stages. In the first stage we estimate for
each good a share equation and a log unit value equation using within-cluster
estimation and instrumental variables in a 2SLS framework.6 In the second
5
Thanks to Philippe De Vreyer for having pointed this out.
There are two reasons here for preferring 2SLS to the more efficient 3SLS procedure.
First, 3SLS risks contaminating the estimates of the share equation by a misspecification
of the unit value equation (or the reverse, but we have more confidence in the validity of
the share specification). Second, 2SLS estimates of the share equations will automatically
satisfy adding-up restrictions, whereas this does not necessarily hold for 3SLS estimates
(see e.g. Bewley, 1986).
Further note that the within-cluster technique adopted will not only sweep away the
6
11
stage we retrieve the price coefficients using between-cluster estimation while
taking account of measurement errors on the unit values. The third stage
imposes the symmetry restrictions through minimum distance estimation.
3.1
First stage
Averaging (8) over households within the cluster c yields
c
wG c = α0G + Z αG +
X
c
c
δGH ln πH
+ βG ln X + uG c .
(10)
H
The vector α
bG and the scalar βbG are recovered from within-cluster estimation, i.e. the estimating equation is obtained by subtracting (10) from (8).
Similarly, forming cluster means from (9)
c
c
c
c
ln VG = a0G + Z aG + ln πG
+ bG ln QG + vG c ,
(11)
bG and bbG result from within-cluster estimation.
a
Endogeneity issues are addressed by use of instrumental variables where
appropriate, as discussed in the data section below. Several variables are
instrumented by cluster means excluding the current observation. We justify
¡
c¢
this technique as follows. In the regression yi − ȳ c = Xi − X β + ui − ūc ,
P
let X̌i = nc1−1 Xj and consider the asymptotic covariance between X̌i and
j∈c
j6=i
ui − ūc : we have
£
¤
£
¤
1
1 X
1
E X̌i (ui − ūc ) = −E X̌i ūc = −
E [Xj uj ] = − E [Xu] ,
nc nc − 1
nc
j∈c
j6=i
which goes to zero when the number of observations per cluster goes to
infinity.
unobservable price indices from the share equations, but also any cluster-specific effect.
At this stage, the independence between cluster effects and prices plays no role, but it
becomes important in the next stage.
12
3.2
Second stage
Our initial approach had been to estimate parameters δGH in the second
stage and to derive estimates of the parameters of interest λG and γGH
for all G and H by minimum distance. The γGH must satisfy symmetry,
P
γGH = γHG , and homogeneity, H γGH = 0, which also implies the addingup restriction. The λ vector is subject to the restrictions λG > 0 and
P
H λH = 1 (positive linear homogeneity of the price index). Besides these
restrictions, the relationships between the parameters of interest (γ, λ) and
the auxiliary parameters ψ = (δ, β) are the m2 equations δGH = γGH −
βG λH . Unfortunately, these restrictions are not sufficient to identify the
parameters of interest, although their number might at first lure one into
thinking they would. Indeed, if (γ, λ) satisfy all the restrictions, so will
(γ̇, λ̇), with γ̇GH (κ) = γGH + κβG βH and λ̇H (κ) = λH + κβH , for all κ
P
such that λ̇H (κ) > 0 for all H, given that H βH = 0. Thus we arbitrarily
set λ = w̄, the vector of average budget shares over all households, which
provides identification of the γ coefficients. The second stage thus consists in
estimating a matrix of γ coefficients conditional on λ = w̄, without imposing
symmetry, the latter being imposed in a third stage by minimum distance.
Separating observables and unobservables in (10) and (11) yields
c
c
c
ηG
≡ wG c − Z α̂G − β̂G ln X
X
∗c
c
+ uG c
= α0G +
(γGH − βG λcH ) ln πH
+ uG c ≡ ηG
(12)
(13)
H
and
c
c
c
c
∗c
c
ζG
≡ ln VG − Z aG − bG ln QG = a0G + ln πG
+ vG c .
+ vG c ≡ ζG
(14)
Only between-cluster information needs to be considered here, since no information on the price responses remains to be exploited within clusters.
13
∗c and the vector ζ ∗c with components ζ ∗c
The true relationship between ηG
H
is
∗c
t
ηG
= ρG + ωG
+
where
t
ωG
=
∗c
(γGH − βG λH ) ζH
,
H
P
t −
σG
X
H
P
(γGH − βG λH ) stH and ρG ≡ α0G − (γGH − βG λH ) a0H ,
H
and thus
∗c
ηG
+
X
∗c
t
βG λH ζH
= ρG + ωG
+
H
This suggests the regression of
c
ηG
+
P
H
X
∗c
γGH ζH
.
H
c
βG λH ζH
on ζ c , time dummies and a
constant. Measurement error bias is caused by the correlation between the
vectors ζ c , vc and possibly uc , but is easily corrected because the variance
of (ucG , vc ) can be estimated as
·
µ c¶
uG
1
Ω̂uG
=
V̂
c
v
nc Ω̂vuG
Ω̂uG v
Ω̂v
¸
,
where each term of Ω̂ is obtained from the first stage residuals. This is
the place where the difficulty of relaxing the homoscedasticity assumption
becomes manifest. Under the assumptions that the λH are known constants
and that β is known, a consistent estimator of the vector γG , after demeaning
√
the η and ζ variables and scaling them by nc , is given by7
γ̂G = [
C
C
X
X
¡ c c
¢
ζ + βG ζ c ζ c0 λ − Ω̂νuG − Ω̂v λ]. (15)
nc ζ c ζ c0 − Ω̂v ]−1 [ nc ηG
c=1
3.3
c=1
Third stage
We estimate symmetry-restricted parameters γ by minimum distance estimation conditional on λ. Following the efficiency arguments of Kodde, Palm
and Pfann (1990, Theorem 5) we minimise only over γ rather than over γ
and β. Given the linearity of the restrictions, the computations boil down
to GLS estimation in the parameter space. This requires an estimate of the
7
Asymptotics here concern the thought experiment where both the number of observations in each cluster nc and the number of clusters C go to infinity.
14
variance of the unrestricted estimator, and a convenient way to obtain this
is to recognise that the procedure of the first two stages falls into the framework of sequential GMM outlined by Newey (1984), as already pointed out
by Deaton (1990). However an attractive alternative lies in bootstrapping
and this is the path we follow. In producing the bootstrap samples we keep
the size of clusters fixed, and the number of bootstrap samples is set equal
to the number of observations.
4
Empirical illustration
We provide an illustration using data from the Czech Family Budget Surveys for 1991 and 1992. Households included in the sample were asked
to maintain an expenditure diary for a full twelve months, recording both
quantities and expenditures for certain goods. The length of the recording
period has the advantage of virtually eliminating infrequency of purchase as
an explanation for zero records on most main expenditure items. However
the burden imposed on participants must have been arduous and we discarded 480 households who did not take part over the full year. The data
is a panel, but the household identifier is not retained between years, necessitating considerable effort to recover and use the panel structure (at best
with imprecision). Households whose circumstances change in any major
way are dropped from the sample — an unfortunate feature which again
diminishes the usefulness of the panel aspect and which must also affect the
cross-sectional sampling properties.
We concentrate in this paper on a subsample of married couples. The
wife’s labour force participation is used as a conditioning variable and instrumented. The sample size obtained in pooling the two years is 4668
households. Given that the number of identifiable geographical clusters is
15
179, we have an average of 26 households per cluster, with a minimum of 7
and a maximum of 60.8
Eight categories of goods were selected for demand estimation. The
choice was constrained by the need to have both quantities and expenditures available. Since we have no reason to believe that the availability of
quantity information — related to the survey design — is directly connected
to the structure of preferences, it is not attractive to assume that the latter
are separable in the corresponding partition. Rather, following Browning
and Meghir (1991), we condition the budget shares (though not the unit
values) of the included goods on the expenditures on the excluded goods.9
Furthermore we will condition the budget shares for the modelled goods on
durable ownership and on a variable describing the labour market status of
the household. In the words of Browning and Meghir:
“The conditional demand system will be correctly specified whether
or not [labour market status] is chosen optimally. Additionally
we do not need to model explicitly the budget constraint for the
conditioning goods. This is particularly significant for labour
supply and for durables [... ] Conditional demand functions are
an economical way of relaxing separability and still maintaining
the focus on the goods of interest.”
Homogeneity with respect to the prices of the excluded goods will be ensured by expressing the conditioning expenditures in relative terms with
respect to one of them, namely housing expenditure.10 The problem of zero
conditioning expenditures is taken care of by the introduction of dummies.
Under weak separability, these conditioning variables should play no role in
8
The reason why we have an uneven number of geographical clusters over the two time
periods is that one of the clusters had too few observations in one of the periods to be
retained in the analysis.
9
Detailed lists of the goods in both categories, including also the exact composition of
each aggregate, are given in Appendix B.
10
Thanks to Arthur Lewbel for pointing this out.
16
the demand equations. The compatibility between this conditional approach
and the unit value model described above is ensured by the fact that the
conditional cost function is amenable to Hicks aggregation.
For some commodities, the survey includes “in kind” quantities and expenditures as well as purchased goods. We treat all quantities together
(purchased or not), evaluating in kind quantities on the basis of the unit
values as an approximation.
Furthermore we condition the budget shares and unit values for the modelled goods on durable ownership and on a variable describing the labour
market status of the household. Other variables used include a wide range
of socio-demographic and housing characteristics.11 We treat as endogenous
the logs of total expenditure X and of quantity QG , the conditioning expenditures and durable ownership variables and labour market status of the
wife. Instruments include the log of income (which should be correlated
with ln X and ln QG ), wife’s age and education, and age of the youngest
child (which should all be correlated with the wife’s participation) and cluster means of the conditioning expenditures and durable ownership excluding
the current observation.
5
Estimates
In Tables 1 and 2, we report the first stage results for all goods along with
their asymptotic standard errors.12 These are the outcome of within-cluster
2SLS regressions of the type explained above: the estimating equations are
11
Descriptive statistics on the variables used are given in Appendix B.
Insofar as we have not, for the compelling reasons outlined above, attempted to identify households present in both years, we should recognise the implications for the validity
of the standard errors. In particular, the inferences drawn are based on inconsistent estimates of the variance of the estimated coefficients. One way out of this difficulty would
be to report results separately for 1991 and 1992, which ought also to be of interest in
their own right.
12
17
obtained by subtracting (10) from (8), and (11) from (9). Note that in the
equations presented for unit values the price effects have been swept away,
so that only the choice component embodied in the unit values is reflected
here.
From the share equations (Table 1) we see that several of the conditioning goods are significant, implying decisive rejection of separability of
preferences in the partition modelled goods / other goods.
The woman’s participation has a significant impact on four budget shares:
on meat and starches a negative impact, and a positive one on clothing and
on footwear, implying also clear rejection of the separability of preferences
in the partition leisure/goods. It has a positive and significant impact on
all unit values, except for the two categories dairy and vegetables/fruit, and
the combined effect on quantity and on unit value of meat and starches as
opposed to clothing and footwear has a neat interpretation. Several other
variables have contrasted effects on quantity and unit value (see e.g. the
effects of education of the household head on the quantity and unit value
of meat purchased), but a complete enumeration would be tedious, and the
reader will be able to browse through the results without our guidance.
Turning to the impact of expenditure on budget shares, for meat, alcohol
and clothing the coefficient of ln X is significantly positive. Budget shares for
vegetables/fruit and for dairy products are significantly negatively affected
by total spending. A test for the absence of the term (ln X)2 rejects the null
for all goods. While this may suggest that a QUAID specification would be
more appropriate, this would not be straightforward to implement, since the
squared term should include the log of real expenditure, and thus involve a
price index in a non-linear fashion, thus defeating within-cluster estimation.
Finally, note that expenditure on tobacco correlates positively with the
18
budget shares on meat and alcohol, negatively with those on dairy, starches
and vegetables/fruit, while expenditure on hygiene and health go the other
way round. All these qualitative results conform with intuition.
From the unit values equations (Table 2) we see that clear evidence of a
relationship between unit value and quantity appears for two goods, dairy
products and starches, where the effect is negative. There is weaker evidence of a positive relationship in the case of vegetables and fruit. The fact
that we obtain significant effects of quantity on unit value implies that the
straightforward instrumenting approach of Pitt (1983) and Strauss (1982)
would, as suggested, be inconsistent.
It is interesting to note the influence of the durable ownership variables:
possession of a freezer, for instance, which is significant in only two of the
food share equations, meat (+) and starches (-), appears to have a significant
influence in five of the food unit value equations, always entering with a
negative sign. To a lesser extent a similar observation can be made for
motor vehicle ownership — while it does not appear to affect budget shares,
there is some evidence that it is associated with lower unit values for some
goods. The most intuitive explanation for both effects is that households
thus equipped have better opportunities for purchasing in large quantities
and for either taking advantage of low price opportunities or searching for
them.
Third stage estimates of the symmetry (and homogeneity, which follows
given adding-up) restricted parameters γGH are given in Table 3. These are
estimated using the measurement error correction procedure at the second
stage.13 The table also reports the minimised value of the criterion, which
provides a χ2 test of the restrictions. We obtain a rejection at any reasonable
13
The underlying second stage estimates are omitted in order to save on space, but are
available on request.
19
level of significance. One possible explanation could be that the restricted
estimates also embody the restriction that the deflator of total expenditure
is a Stone price index which varies across clusters, but with fixed weights.
Given our focus on a sample of married couples, a more direct source of this
rejection may lie in the misspecification of the unitary model of household
preferences, as forcefully documented by Browning and Chiappori (1998),
who reject symmetry for couples but not singles on Canadian data.
Marshallian elasticities based on the first and third stage estimates and
computed at mean sample using the formulae
eGH
= (γGH − βG w̄H ) /w̄G − 1[G=H] ,
eG = 1 + βG /w̄G ,
are reported in Table 4. Expenditure elasticities for all goods are significantly different from zero. Dairy, vegetable and fruit and alcohol categories
present elasticities which differ significantly from one, classifying alcohol as
a luxury, dairy, vegetables and fruit as necessities. A surprise is perhaps
the low budget elasticity of the vegetable and fruit category, which is at
variance with results typically found for other countries. All but one of the
(uncompensated) own price elasticities are negative and several are significantly different from zero. Several significant cross price effects are also
observed.
The only point of reference we have in assessing these elasticities is the
work of Ratinger (1995), based on monthly data on 300 households of employees from January 1990 to September 1992, apparently using published
average expenditures on food.14 Given the differences between the two studies, concerning data and methodologies, the comparison is difficult. For in14
The paper gives no information on the nature of the price data used.
20
stance, depending on the degree of aggregation of goods, Ratinger reports
expenditure elasticities between .98 and 1.14 for meat.
21
22
-2.8
3.3
5.2
6.7
-5.5
2.9
-.7
-2.6
1.9
3.8
-4.9
2.0
2.1
.6
.7
3.0
3.4
.4
-1.5
-1.0
.4
1.4
-3.9
-4.4
-.2
-5.4
.8
4.6
-2.0
-7.6
-5.9
-4.7
.7
1.0
-1.2
2.3
.140
.039
.593
.759
.101
-.317
-.191
.093
.299
-.693
-1.96
-.042
-1.20
.149
.246
-.636
-.900
-.461
-.352
1.10
.461
-.905
ln(Total expenditure)
5.31
Notes: All coefficients × 100
t
-3.98
.819
1.62
5.36
-.494
.726
-.178
-1.07
.051
.831
-1.43
.571
.025
Household characteristics
Wife’s participation
Blue collar
Farmer
Age of head of household
Age of hoh squared
Owner-occupier
No mod-cons
Number of. hh members
Average age of children
Basic education - hoh
Advanced education - hoh
Rural
Space per person
Durable ownership
Gas supplied
Number of leisure durables
Freezer
Phone
Car or motor bike
Automatic washing machine
Food processor
Caravan and/or dacha
Garage
Conditioning expenditures
ln(Transport)
ln(Hygiene)
ln(Food out)
ln(Culture)
ln(Fuel)
ln(Tobaccco)
ln(Other food)
ln(Textiles)
ln(Medical)
ln(Furniture)
No food out
No Tobacco
No Medical
Meat
Coeff
-8.55
.339
.878
-.323
-.344
.261
-.223
.543
-.275
.128
-.087
-2.39
-.735
-.040
-.717
-.092
-.092
-.363
-.189
.313
.280
-.202
-.045
-1.25
.170
.173
.948
-.028
.554
.202
1.84
.020
-.569
-.172
-.037
.013
t
-5.5
2.4
2.9
-2.2
-2.2
1.7
-5.9
2.4
-3.4
2.5
-1.6
-2.2
-2.3
-.1
-4.2
-2.4
-.7
2.4
-1.1
2.0
2.2
-1.2
-.3
-1.3
1.0
.8
1.7
-.5
3.2
1.1
6.7
1.1
-3.7
-.8
-.2
1.6
Dairy
Coeff
-2.28
.008
-.977
.046
-.065
.287
-.077
-.054
-.260
.158
-.075
1.03
-.773
.472
-.299
003
-.261
-.202
-.202
-.057
-.201
.267
-.196
-2.08
.157
.388
1.38
-.091
.338
.169
1.00
.063
219
-.386
.290
.012
-1.9
.1
-4.2
.4
-.6
2.2
-2.9
-.3
-4.3
3.9
-1.9
1.0
-3.3
1.3
-2.3
.1
-2.6
-1.8
-1.5
-.5
-2.2
2.1
-1.8
-2.7
1.2
2.3
3.5
-2.0
2.6
1.2
4.6
4.5
1.9
-2.6
1.9
1.7
Starches
Coeff
t
-4.85
.193
1.06
-.128
-.003
-.021
-.150
1.09
.094
.222
-.030
-1.12
-.543
.047
-.162
-.017
.043
-.041
-.109
.006
.099
-.281
-.009
1.23
-.095
-.305
.055
.060
-.519
.274
.422
-.026
.060
-.012
-.486
-.013
-4.1
1.9
4.4
-1.2
-.0
-.2
-5.4
6.2
1.6
5.8
-.7
-1.4
-2.1
.1
-1.3
-.6
.4
-.3
-.8
.1
1.1
-2.2
-.1
1.6
-.8
-2.1
.1
1.3
-4.3
2.0
2.0
-1.9
.5
-.1
-3.6
-2.2
Veg/Fruit
Coeff
t
Table 1: Engel curves
-1.36
.034
.536
-.018
.059
.104
-.023
.363
-.132
.108
-.040
.405
.065
.483
-.222
.002
-.076
-.029
.052
-.003
.001
-.156
-.073
.081
-.022
-.070
.237
.007
-.159
-.039
.229
-.019
.099
-.098
.077
.011
t
-1.6
.5
3.4
-.2
.8
1.7
-1.2
3.0
-3.2
4.0
-1.5
.7
.4
1.8
-2.4
.1
-1.1
-.4
.6
-.0
.0
-1.7
-1.0
.1
-.3
-.6
.9
.2
-1.8
-.4
1.5
-1.9
1.3
-.9
.8
2.2
Sweet
Coeff
4.29
-.209
-1.02
.491
.419
.036
.293
-.120
-.250
-.088
.067
2.15
.671
-.050
.267
.152
.277
.013
-.308
-.010
-.494
.481
-.422
-1.61
-.261
.249
1.84
-.255
-.086
-.149
-1.631
-.090
.022
.034
.571
-.005
t
2.2
-1.3
-2.7
2.8
2.4
.2
6.5
-.4
-2.4
-1.4
1.0
1.7
1.8
-.1
1.2
3.3
1.7
.1
-1.4
-.1
3.3
2.2
-2.4
-1.3
-1.2
1.1
2.6
-3.3
-.4
-.7
-4.7
-4.1
.1
.1
2.6
-.5
Alcohol
Coeff
8.02
.323
.986
-.094
.938
-.697
-.064
-1.05
1.47
-.028
.437
-1.08
.793
.260
.680
-.027
-.361
-.183
.662
-.022
.372
-.167
.348
5.91
-.495
-1.54
-7.87
.638
-.872
-.359
-1.30
.002
-.682
1.75
-.800
-.035
3.1
1.5
1.9
-.4
3.8
-2.8
-1.0
-2.7
10.2
-.3
4.8
-.6
1.6
.3
2.4
-.4
-1.6
-.7
2.3
-.1
1.8
-.6
1.4
3.8
-1.7
-4.3
-9.0
6.7
-3.1
-1.2
-2.8
.1
-2.7
5.0
-2.6
-2.5
Clothes
Coeff
t
-.578
006
.487
.068
.197
-.118
-.003
-.129
.258
-.038
.080
-.097
.061
-.268
.312
-.060
-.124
.045
-.006
.089
.133
-.035
.097
1.70
-.273
-.516
-1.95
.163
.018
.081
.506
-.001
.019
.316
-.187
-.008
t
-.5
.1
2.4
.7
2.0
-1.0
-.1
-.8
4.2
-1.0
2.0
-.1
.3
-.8
2.5
-2.3
-1.3
.4
.0
.8
1.5
-.3
1.0
2.5
-2.3
-3.6
-5.2
4.0
.2
.6
2.7
-.1
.2
2.3
-1.4
-1.6
Shoes
Coeff
23
ln(Quantity)
Notes: All coefficients × 100
Household characteristics
Wife’s participation
Blue collar
Farmer
Age of head of household
Age of hoh squared
Owner-occupier
No mod-cons
Number of hh members
Average age of children
Basic education - hoh
Advanced education - hoh
Rural
Space per person
Durable ownership
Gas supplied
Number of leisure durables
Freezer
Phone
Car or motor bike
Automatic washing machine
Food processor
Caravan and/or dacha
Garage
.9
2.9
-.1
-2.4
-.2
-1.9
1.2
-1.0
-2.3
1.6
1.35
-.009
-.904
-.089
-.836
.500
-.370
-1.06
.818
1.47
4.2
-1.6
-1.2
-1.6
1.1
-.5
-2.1
-1.2
-1.3
-1.7
5.0
-.5
-.5
t
4.65
-.718
-.741
-2.81
.189
-.318
-1.27
-.421
-.059
-.746
2.54
-.222
-.013
Meat
Coeff
-9.68
-.353
.216
-.266
1.195
-2.89
2.20
-.967
-.877
-.014
1.839
-3.01
-7.26
-10.4
.745
.994
-.181
1.024
-.101
-2.32
6.09
-1.56
-.215
t
-2.2
-.3
.9
-.3
1.3
-2.7
2.3
-1.2
-.8
.0
0.7
-2.8
-5.2
-2.8
1.9
.9
-.2
1.3
-1.0
-2.1
4.8
-1.3
-4.3
Dairy
Coeff
-6.92
.558
.333
-2.50
.627
-1.15
.513
-.220
.291
-.722
6.72
-1.45
-2.46
-12.3
1.20
-2.30
.023
1.79
-.103
-.460
2.69
-2.35
-.074
-2.3
.8
2.2
-4.4
1.1
-1.7
.8
-.4
.4
-1.2
3.8
-2.0
-2.6
-5.3
5.0
-3.4
.0
3.6
-1.5
-.7
3.1
-3.1
-2.3
Starches
Coeff
t
12.4
989
-.317
-5.51
156
-1.73
997
-2.64
-1.20
-2.11
692
-.080
-6.16
-12.4
.870
-2.13
-1.34
-1.94
-.500
-.425
2.28
-2.85
-.112
1.9
1.0
-1.4
-6.8
.2
-1.7
1.1
-3.5
-1.2
-2.5
.3
-.1
-4.0
-3.0
2.2
-1.9
-1.3
-1.8
-5.0
-.4
1.7
-2.4
-2.0
Veg/Fruit
Coeff
t
-10.1
-.960
.461
-2.63
-1.21
1.30
.601
3.04
.725
.337
8.23
1.03
.469
-8.34
.928
-3.02
-2.27
3.58
-.128
1.04
-1.01
-1.73
.070
t
-1.1
-.7
1.5
-2.1
-1.0
.9
.5
2.9
.5
.3
2.4
.7
.2
-1.5
1.7
-2.0
-1.5
2.4
-.9
.7
-.5
-1.1
1.0
Sweet
Coeff
Table 2: Unit value equations
-3.22
2.59
.949
-2.99
1.158
-2.871
2.513
2.75
-6.36
-2.37
23.3
-3.23
-7.79
-34.3
3.24
-5.60
-3.46
1.66
-.345
-4.96
6.44
-3.34
-.006
-.2
1.4
2.4
-2.0
.8
-1.6
1.5
2.2
-3.6
-1.6
5.4
-1.7
-2.9
-4.4
4.6
-3.0
-2.0
.6
-1.9
-2.4
2.6
-1.8
-.1
Alcohol
Coeff
t
20.3
1.81
.746
.680
-2.425
5.359
-1.650
-.700
-1.168
2.860
38.1
-4.61
-4.41
-34.3
3.50
.639
1.62
-5.45
.189
-4.01
6.54
-.879
-.142
.7
.8
1.6
.3
-1.4
2.7
-.8
-.5
-.6
1.7
6.8
-2.0
-1.1
-2.7
3.4
.2
.7
-1.3
.9
-1.3
1.7
-.4
-1.1
Clothes
Coeff
t
5.89
1.76
.046
-.542
-.825
-.014
-1.03
-.451
-.766
.107
46.3
-2.92
-4.78
-12.8
1.60
-4.50
-.000
-12.2
1.44
-3.54
2.71
-4.55
-.021
t
.2
.7
.1
-.2
-.5
-.0
-.5
-.3
-.3
.1
7.0
-1.2
-1.0
-.8
1.3
-1.6
-.0
-2.5
6.3
-1.0
.6
-1.8
-.1
Shoes
Coeff
Table 3: Symmetry restricted estimates of γ
Meat
Dairy
Starches
Veg/Fruit
Sweet
Alcohol
Clothes
Shoes
Meat
1.764
3.016
-9.882
1.507
-3.061
1.292
-10.320
1.332
2.723
0.941
1.489
0.820
10.564
1.472
6.724
0.986
Dairy
Starches
Veg/Fruit
Sweet
Alcohol
Clothes
Shoes
15.905
1.403
-2.056
0.813
4.471
0.808
-0.669
0.591
0.462
0.537
-8.211
0.936
-0.021
0.611
3.551
1.245
-1.892
0.736
1.577
0.549
-0.545
0.432
1.134
0.775
1.293
0.550
17.383
1.147
-1.013
0.531
3.066
0.473
-8.530
0.844
-3.164
0.572
0.102
0.581
0.906
0.324
-2.994
0.551
-0.631
0.386
-2.634
0.861
-1.916
0.819
-0.827
0.361
12.879
1.836
-2.926
0.622
-0.448
0.623
Notes: All coefficients and standard errors × 100.
Standard errors below coefficients.
Wald test of symmetry restrictions χ228 = 351.29 (Critical value at 5% is 41.34).
24
25
Price
Meat
Dairy
Starches Veg/Fruit
Sweet Alcohol
Clothes
Meat
-0.968 -0.428
-0.145
-0.424
0.095
0.041
0.381
0.118
0.066
0.053
0.054
0.038
0.035
0.064
Dairy
-0.463
-0.062
-0.064
0.309
-0.009
0.070
-0.403
0.100
0.086
0.050
0.056
0.036
0.034
0.070
Starches
-0.231
-0.151
-0.721
-0.158
0.159
-0.033
0.141
0.121
0.081
0.122
0.069
0.052
0.042
0.079
Veg/Fruit -1.003
0.591
-0.146
1.067
-0.080
0.382
-0.848
0.148
0.095
0.082
0.130
0.059
0.055
0.102
Sweet
0.566
-0.077
0.321
-0.167 -1.078
0.188
-0.510
0.174
0.116
0.103
0.099
0.117
0.063
0.112
Alcohol
0.052
-0.042
-0.130
0.340
0.081
-1.407
-0.331
0.119
0.083
0.061
0.065
0.044
0.132
0.117
Clothes
0.414 -0.469
0.010
-0.444 -0.168
-0.125
-0.275
0.078
0.055
0.040
0.045
0.028
0.042
0.096
Shoes
1.218
0.015
0.241
-0.553
-0.106
-0.138
-0.501
0.187
0.118
0.100
0.107
0.070
0.068
0.124
Note: Standard errors below coefficients
Bold entries correspond to rejection of H0 : e=0; for expenditure elasticities, rejection of
for dairy, veg/fruit and alcohol.
Table 4: Marshallian elasticities
Total
budget
1.195
0.116
0.596
0.113
0.864
0.134
0.356
0.133
0.860
0.165
1.570
0.276
1.219
0.154
0.842
0.229
H0 : e=1 occurs
Shoes
0.254
0.040
0.026
0.037
0.131
0.053
-0.320
0.065
-0.103
0.073
-0.132
0.049
-0.162
0.032
-1.018
0.125
6
Conclusion
We have presented a new approach to the estimation of demand systems on
the basis of unit values and have argued that its advantage over Deaton’s
approach, which also treats unit values as consumer choice variables, is
improved consistency with demand theory, while its advantage over the
naive treatment of unit values as erre-ridden measurements of prices is improved statisticla consistency. Monte Carlo experiments designed to compare its performance with alternative methods are presented by Lahatte et
al. (1998). They do suggest that our theory-consistent specification for the
log unit value equation outperforms Deaton’s first order Taylor expansion,
but that both specifications may perform poorly when data are generated
by a more flexible form.
Another advantage of our approach over alternatives is its relative computational simplicity, the main difference residing in the second stage where
we can treat goods separately whereas a system estimation is necessary in
Deaton’s approach. This simplification may allow us to consider more complicated settings, where for instance spatial patterns of consumption are of
primary interest. In this respect, it is interesting to note that in her work
on spatial aspects of consumption, and while aware of Deaton’s work, Case
(1991) chooses to treat unit values as error-ridden measurements of prices
rather than to model them as the outcome consumer choices. Combining,
on one side, a proper treatment of the fact that unit values are outcomes of
choice and, on the other side, the spatial patterns of demand, would seem a
rewarding endeavour.
Interestingly our proposal resembles Lewbel’s (1989) approach to the
identification and estimation of demand systems in the absence of price
variation in several respects. Lewbel makes the same homothetic weak sep26
arability assumption and develops a method allowing price indices, constructed from budget share estimation at the lower level even without price
variation, to be used to estimate unrestricted upper level demand equations.
An appealing extension would thus combine both approaches. A possibility
would apply our within-cluster techniques using more disaggregated unit
value information at the lower level15 , allowing a freeing up of the demand
specification at the higher level in the fashion proposed by Lewbel. Finally it would also obviously be interesting to introduce these techniques in
a collective model of household consumption as the rejection of symmetry
suggests.
15
Table 7 indicates the finest level of disaggregation at which unit value information is
available in the Czech data
27
Appendix A. Implications of the same log-linear
specification for shares and log unit values
Suppose the share equations are derived from the AID functional form,
wG = αG +
X
δGH ln πH + βG ln X + uG ,
H
and that the log unit values have a similar form
ln VG = AG +
X
DGH ln πH + BG ln X + UG ,
H
as in Deaton (1990). Then
∂ ln QG /∂ ln πH
∂ ln QG /∂ ln X
∂ ln ξG /∂ ln πH
∂ ln ξG /∂ ln X
=
=
=
=
∂ (ln wG − ln VG ) /∂ ln πH
∂ (ln wG + ln X − ln VG ) /∂ ln X
∂ (ln VG − ln πG ) /∂ ln πH
∂ (ln VG − ln πG ) /∂ ln X
=
=
=
=
δGH /wG − DGH ,
βG /wG + 1 − BG ,
DGH − 1[G=H] ,
BG .
Hence, by (4), considering first the case where G 6= H :
hD
δGH − wG
DGH
GH
=
,
h
BG
βG + wG (1 − BG )
where both denominators are assumed different from 0. This implies
h
DGH wG
= BG δGH − βG DGH .
h and all G and H 6= G requires D
For this to hold for all wG
GH = δGH = 0,
since BG 6= 0. Thus in both equations only the own price is included. But
turning to the case G = H, we see that the restriction is even more severe,
because then for all G
DGG − 1
δGG − wG DGG
=
,
βG + wG (1 − BG )
BG
which implies
BG = 1 − DGG ,
βG = −δGG ,
so that in the end there is only one free slope parameter in each equation.
28
Appendix B. Data
Tables 5 and 6 presents descriptive statistics for the variables used, Table 7
gives the precise definition of goods.
Table 5: Descriptive statistics (Modelled goods)
Budget shares
Good
Meat
Dairy
Starches
Veg/Fruit
Sweet
Alcohol
Clothes
Shoes
Mean
0.250
0.185
0.116
0.081
0.060
0.083
0.172
0.053
Std Dev
0.069
0.045
0.035
0.032
0.022
0.052
0.082
0.031
ln Quantity
Mean
5.107
6.723
6.064
5.060
4.963
4.791
4.022
1.916
29
Std Dev
0.425
0.425
0.437
0.507
0.649
1.018
0.606
0.760
ln Unit value
Mean
3.957
2.052
2.229
2.839
2.651
2.980
4.564
5.423
Std Dev
0.141
0.312
0.196
0.247
0.391
0.473
0.457
0.525
Table 6: Descriptive statistics (Explanatory variables)
Variable
Household characteristics
Wife’s participation
Blue collar
Farmer
Age of head of household
Age of hoh squared
Owner-occupier
No mod-cons
Number of. hh members
Average age of children
Basic education - hoh
Advanced education - hoh
Rural
Space per person
ln(Total expenditure)
ln(Income)
Durable ownership
Gas supplied
Number of leisure durables
Freezer
Phone
Car or motor bike
Automatic washing machine
Food processor
Caravan and/or dacha
Garage
Conditioning expenditures
ln(Transport)
ln(Hygiene)
ln(Food out)
ln(Culture)
ln(Fuel)
ln(Tobaccco)
ln(Other food)
ln(Textiles)
ln(Medical)
ln(Furniture)
No food out
No Tobacco
No Medical
30
Mean
Std Dev
0.734
0.401
0.234
4.361
0.442
0.394
0.169
3.252
6.210
0.472
0.174
0.325
26.392
10.491
11.485
0.442
0.490
0.424
1.193
11.415
0.489
0.374
1.024
6.013
0.499
0.379
0.469
11.535
0.304
0.302
0.525
4.298
0.568
0.351
0.803
0.775
0.444
0.192
0.465
0.499
1.849
0.495
0.477
0.398
0.418
0.497
0.394
0.499
7.734
8.037
7.817
8.247
5.316
4.558
8.314
7.113
5.027
8.041
0.026
0.202
0.045
0.674
0.487
1.714
0.832
3.567
3.216
0.513
1.041
1.828
1.380
0.160
0.401
0.207
31
Other textile
Housing
Medical
Furniture and equipment
Energy
Tobacco
Other food
Shoes
Conditioning goods
Transport and communication
Hygiene
Meals out
Culture and recreation
Sweet
Alcohol
Clothes
Veg/Fruit
Starches
Dairy
Modelled goods
Meat
commuting to work, other public transport, telephone etc.
soaps, detergents, cosmetics, toiletries, laundry, home help, dry cleaning, hairdresser, cosmetics.
company canteens, school canteens, restaurants, other catering.
books, magazines, toys, culture articles (durable), (non durable), sports equipment, tourist accommodation,
flowers, other personal services, education, culture, sports, entertainment, creche, kindergarten,
recreation inside Czech Republic, recreation abroad, other services.
fuel all types, electricity, gas, central heating and other municipal services.
tobacco products.
confectionery, coffee, tea, ready to cook foods, powdered food, other food.
in kind: other foods and beverages, free catering
textiles, furs, haberdashery, leatherware, tailoring services.
rent, maintenance, cooperative flat payment.
medicines and health care goods, medical treatment.
furniture, soft furnishings, glass, porcelain, pots and pans, refrigerators, freezers, electric
razors, hairdryers, washing machines, dryers.
pork, beef, other meats and offal, poultry, canned meat, other meat products, fresh and canned fish.
in kind: pork, other meat and meat products, poultry.
butter, margarine, vegetable oil, eggs, bacon and lard, milk, cheese, other milk products.
in kind: eggs, bacon and lard, milk.
potatoes, bread, bakery products, wheat flour, other cereal products, rice, pulses.
in kind: potatoes.
fresh vegetables, frozen vegetable products, fresh fruit, tropical fruit, frozen and dried fruit.
in kind: fresh vegetables, fresh fruit
sugar, chocolate, syrup and concentrates, non-alcoholic beverages.
beer, wine, other alcoholic drinks.
cloth or fabric, stockings/socks, knitwear for adults and for children, knit clothes for adults and for children,
ready to wear clothing for adults and for children.
men’s, women’s, and children’s shoes.
Table 7: Description of goods
References
[1] Ayadi, Mohamed, Rafiq Baccouche, Mohamed Goaied and Mohamed
S. Matoussi, 1995. Spatial Variations of Prices and Household Demand
Analysis in Tunisia, paper presented at the 7th World Congress of the
Econometric Society, Tokyo.
[2] Ayadi, Mohamed, Jaya Krishnakumar and Mohamed S. Matoussi, 2002.
Pooling Surveys in the Estimation of Income and Price Elasticities:
An Application to Tunisian Households, forthcoming, Empirical Economics.
[3] Banks, James, Richard Blundell and Arthur Lewbel, 1996. Tax Reform
and Welfare Measurement: Do We Need Demand System Estimation?,
Economic Journal, 106, 1227-1241.
[4] Banks, James, Richard Blundell and Arthur Lewbel, 1997. Quadratic
Engel Curves and Consumer Demand, Review of Economic and Statistics, 4, 527-539.
[5] Bewley, Ronald, 1986. Allocation Models: Specification, Estimation and
Applications. Cambridge, Mass.: Ballinger.
[6] Browning, Martin J. and Costas D. H. Meghir, 1991. The Effects of Male
and Female Labour Supply on Commodity Demands, Econometrica, 59,
925-952.
[7] Browning, Martin J. and Pierre-André Chiappori, 1998. Efficient IntraHoursehold Allocations: A General Characterization and Empirical
Tests, Econometrica, 66, 1241-1278.
[8] Case, Anne, 1991. Spatial Patterns in Household Demands, Econometrica, 59(4), 953-65.
[9] Deaton, Angus S., 1987. Estimation of Own and Cross-Price Elasticities
from Household Survey Data, Journal of Econometrics, 36, 7-3.
[10] Deaton, Angus S., 1988. Quality, Quantity and Spatial Variation of
Price, American Economic Review, 78, 418-43.
[11] Deaton, Angus S., 1990. Price Elasticities from Survey Data: Extension
and Indonesian Results, Journal of Econometrics, 44, 281-309.
[12] Deaton, Angus S., 1997. The Analysis of Household Surveys: A Microeconometric Approach to Development Policy, Baltimore: John Hopkins
University Press for the World Bank.
32
[13] Deaton, Angus S. and Franque Grimard, 1991. Demand Analysis for
Tax Reform in Pakistan, Discussion Paper No 151, Research Programme in Development Studies, Centre for International Studies,
Woodrow Wilson School, Princeton.
[14] Deaton, Angus S. and John N. J. Muellbauer, 1980. Economics and
Consumer Behavior. Cambridge: Cambridge University Press.
[15] De Vreyer, Philippe, 2000, Coûts unitaires et estimation d’un système
de demande de travail: théorie et application au cas de Taiwan”, Annales d’Économie et de Statistique, 57, 211-238.
[16] Kodde, David A., Franz C. Palm and Gerard A. Pfann, 1990. Asymptotic Least-Squares Estimation Efficiency Considerations and Applications, Journal of Applied Econometrics, 5, 229-243.
[17] Jorgenson, Dale W., Lawrence J. Lau and Thomas M. Stoker, 1982.
The Transcendental Logarithmic Model of Aggregate Consumer Behavior, in Basmann, Robert L. and George F. Rhodes (eds.) Advances
in Econometrics, Vol.1, 97-238. Greenwich: JAI Press.
[18] Lahatte, Agénor, François Laisney, Ruth Miquel and Ian Preston, 1998.
Demand Systems with Unit Values: a Comparison of Two Specifications, Economics Letters, 58(3), 281-290.
[19] Lewbel, Arthur, 1989. Identification and Estimation of Equivalence
Scales under Weak Separability, Review of Economic Studies, 56, 311316.
[20] Lewbel, Arthur, 1993. Stochastic Hicksian Aggregation with an Application to Grouping Goods Without Separable Utility, Annales
d’Économie et de Statistique, 29, 17-42.
[21] Lewbel, Arthur, 1996. Aggregation Without Separability: A Generalized Composite Commodity Theorem, American Economic Review, 86,
524-543.
[22] Newey, Whitney K., 1984. A Method of Moments Interpretation of
Sequential Estimators, Economics Letters, 14, 201-206.
[23] Nichèle, Véronique and Jean-Marc Robin, 1995. Simulation of Indirect
Tax Reforms Using Pooled Micro and Macro French Data, Journal of
Public Economics, 56(2), 225-44.
[24] Pashardes, Panos, 1993. Bias in the Estimation of the Almost Ideal Demand System with the Stone Index Approximation, Economic Journal,
103, 908-916.
33
[25] Pitt, Mark M., 1983. Food Preferences and Nutrition in Rural
Bangladesh, Review of Economics and Statistics, 65, 105-14.
[26] Stone, J. Richard N., 1954. The Measurement of Consumers’ Expenditures and Behaviour in the United Kingdom, Cambridge: Cambridge
University Press.
[27] Strauss, John, 1982. Determinants of Food Consumption in Rural Sierra
Leone, Journal of Development Economics, 11, 327-53.
34